Problem: Rewrite as a simplified fraction. ${3.5\overline{31} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}1000x &= 3531.3131...\\ 10x &= 35.3131...\end{align*}}$ Subtracting the two equations, we have: ${990x = 3496}$ ${x = \dfrac{3496}{990}} $ ${x = \dfrac{1748}{495}} \text{or} {3 \dfrac{263}{495}}$